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 A076704 Numbers k of the form p^q where both p and q are prime and all digits of k are odd. 3
 9, 1331, 357911, 5177717, 5735339, 9393931, 17171515157399, 335571975137771, 7979737131773191, 13337513771953951, 13137917533317175739371379, 33159599371999557199755557, 1593395573971551557179777111133, 131755773357537951113179771515713, 315113377779977515359339551539771 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Up to 10^17, there are only 10 odd-digit prime powers of prime numbers. a(1) = 3^2, a(2) = 11^3, a(3) = 71^3, a(4) = 173^3, a(5) = 179^3, a(6) = 211^3, a(7) = 25799^3, a(8) = 69491^3, a(9) = 199831^3, and a(10) = 237151^3. The only candidates for even-digit prime powers of prime numbers are of the form 2^n, and below 2^10000 there are only 2, 4, 8, 64, and 2048, two of which are not raised to prime powers. a(11) <= 13137917533317175739371379 and a(12) <= 33159599371999557199755557. - Jinyuan Wang, Mar 02 2020 LINKS Giovanni Resta, Table of n, a(n) for n = 1..36 (terms < 10^57) MATHEMATICA pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^17]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^17]]]}]]]; Do[ If[ Union[ OddQ[ IntegerDigits[ pp[[n]]]]] == {True}, Print[ pp[[n]]]], {n, 1, Length[pp]}] PROG (PARI) lista(nn) = {my(k, v=List([])); forprime(p=2, nn, forprime(q=2, logint(nn, p), if(Set(digits(k=p^q)%2)==[1], listput(v, k)))); Set(v); } \\ Jinyuan Wang, Mar 02 2020 CROSSREFS Cf. A014261, A053810, A075308. Sequence in context: A020261 A266864 A076442 * A117053 A270067 A213448 Adjacent sequences:  A076701 A076702 A076703 * A076705 A076706 A076707 KEYWORD nonn,base AUTHOR Zak Seidov, Oct 26 2002 EXTENSIONS Edited and extended by Robert G. Wilson v, Oct 31 2002 Corrected and edited by Elliott Line, Jul 11 2013 Better definition from Jon E. Schoenfield, Nov 19 2018 Terms a(11) and beyond from Giovanni Resta, Mar 03 2020 STATUS approved

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Last modified July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)